Probability

MM4D1

Essential Question…

• How do I find the theoretical probability of an event and apply the fundamental counting principle?

Probability

P(A) = ___outcomes desired______ total possible outcomes

***write your answer as a reduced fraction but be ready to convert it to a percent!!

Example 1

A box contains 8 blue marbles, 5 red marbles, and 2 orange marbles. What is the probability of randomly selecting an orange marble in one draw? What is the probability of drawing a marble that is NOT red?

• 2/15• 10/15 = 2/3

Example 2

John sits down to dinner sometime between 6:00 pm and 7:00pm.

A) Find the probability that he will eat from 6:10 to 6:30.

B) From 6:45 to 6:55?• 20/60 = 1/3• 10/60 = 1/6

Example 3

Find the probability that a card chosen at random from a standard deck IS NOT an 8 or an ace.

• 4 “8’s”• 4 “Aces”• 52-8 = 44• 44/52 = 11/13

Example 4

Find the probability that a card chosen at random from a standard deck is the 7 of hearts.

• 1/52

Fundamental Counting Principle

• If there are m ways that one event can occur and n ways that another event can occur, then there are m • n ways that both events can occur.

Example 5

Amy must choose a password for her voice mail. Each letter or digit may be used more than once but she decides not to use “A” and “Z” or “0” and “9”. How many possible passwords exist if she uses 3 letters followed by 3 digits?

24•24•24•8•8•8 = 7,077,888

Example 6

Find the number of possible passwords for the following condition:

4 digits followed by 2 letters

10•10•10•10•26•26

6,760,000

Assignment

• Pg 633-634 #’s 9-33 ALL (omit 24 and 25)

Do Now:

• Find the probability of drawing a 4 from a standard deck.

• How many possible passwords exist if you use 2 digits and 3 letters without using the number 5 or the letter Q?

Pg. 633-634, 9-33 (omit 24-25)

9. 3/10, 30%10. 1/5, 20%11. ½, 50%12. 1/6, 17%13. 1/6, 17%14. ½, 50%15. ½, 50%16. 1/3, 33%17. ½, 50%18. 0, 0%19. 5/6, 83%

20. 1/5, 20%21. 3/5, 60%22. 4/5, 80%23. 2/5, 40%26. 17,576,00027. 6,760,00028. 17,576,00029. 6,760,00030. 3/11, 27%31. 4/9, 44%32. 3/10, 30%33. 1/21, 5%

Tree Diagrams

A lunch special is a hamburger combo. It comes with a choice of beverage (soda or tea) and a choice of salad (garden, chef, or caesar). How many different choices do you have?